Results 1 to 3 of 3

Math Help - Limits question

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    55

    Limits question

    Determine the limit:

    lim x→−3 √ (x^2 + 7 − 4)/(x^2 − 9)

    So I'm pretty sure it doesn't exist but i just wanted to make sure... i got it down to

    √(x^2+3)/(x+3)(x-3)

    which doesn't exist because it equals zero

    thanks for any help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by smplease View Post
    Determine the limit:



    lim x→−3 √ (x^2 + 7 − 4)/(x^2 − 9)

    So I'm pretty sure it doesn't exist but i just wanted to make sure... i got it down to

    √(x^2+3)/(x+3)(x-3)

    which doesn't exist because it equals zero

    thanks for any help
    \lim_{x\to{-3}}\frac{\sqrt{x^2+3}}{x^2-9}

    Multiplying by \frac{\frac{1}{\sqrt{x^2}}}{\frac{1}{\sqrt{x^2}}}

    You will get the answer to be either infinity or undefined..whichever your instructor prefers

    This is because
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by smplease View Post
    Determine the limit:


    lim x→−3 √ (x^2 + 7 − 4)/(x^2 − 9)

    So I'm pretty sure it doesn't exist but i just wanted to make sure... i got it down to

    √(x^2+3)/(x+3)(x-3)

    which doesn't exist because it equals zero

    thanks for any help
    For convenience, let f(x) = √(x^2+3)/(x+3)(x-3).

    Note that \lim_{x \rightarrow -3^+} f(x) = -\infty but \lim_{x \rightarrow -3^-} f(x) = + \infty.

    The left hand limit does not equal the right hand limit.

    Therefore \lim_{x \rightarrow -3} f(x) = +\infty does not exist.
    Last edited by mr fantastic; May 14th 2008 at 12:15 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question about limits
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 19th 2011, 02:23 PM
  2. Limits question
    Posted in the Calculus Forum
    Replies: 11
    Last Post: February 7th 2010, 08:39 AM
  3. limits question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: January 18th 2010, 02:04 PM
  4. Limits question
    Posted in the Calculus Forum
    Replies: 6
    Last Post: February 20th 2009, 05:55 AM
  5. Limits Question...
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: September 19th 2008, 11:49 PM

Search Tags


/mathhelpforum @mathhelpforum